Help please on this Math! 10 points

If tanA = 2/3 and sinB = 5/√41 and angles A and B are in Quadrant I, find the value of tan(A + B)

Thanks in Advance!

sinB = 5/sqrt(41)
==> sin^2(B) = 25/41
cos^2(B) = 1 - sin^2(B) = 1 - 25/41 = 16/41
since it is in quadrant 1
cosB = 4/sqrt(41)

tanB = sinB/cosB = [5/sqrt(41)]/[4/sqrt(41)] = 5/4

tan(A + B) = (tanA + tanB)/(1 - tanAtanB)
tan(A + B) = (2/3 + 5/4)/(1 - 2/3*5/4)
tan(A + B) = (23/12)/(1 - 5/6)
tan(A + B) = (23/12)/(1/6) = 23/2 <==== Answer